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Someone who thinks that the quadratic equation is an empty manipulation, devoid of any other significance, is someone who is content with leaving the many in ignorance. I believe also that he or she is also pleading for the lowering of standards. A quadratic equation is not like a bleak room, devoid of furniture, in which one is asked to squat. It is a door to a room full of the unparalleled riches of human intellectual achievement. If you do not go through that dooror if it is said that it is an uninteresting thing to domuch that passes for human wisdom will be forever denied you.
Throughout human history, that door was locked to those of the working classes, to women and to those who come from nations that were enslaved. Now at last we have a society and culture that have made it possible for people on the largest scale to understand at a most fundamental level the culture they have inherited and the debts that they owe to their forebears. Now we have a society in which many citizens can be empowered to understand the natural world.
Siren voices still aver that many cannot cope with quadratic equations and similar structures, and with the worlds that they unlock. It is the Government's job to resist those who would devalue the educational currency in this way. An educational curriculum that is too undemanding cheats those who could have gained understanding, but who are denied that opportunity. Sadly, those who have been so cheated do not even know what it is that they do not know. If real education can be mentally taxing and painful, that is also one of its greatest values. Those who have profited from it are grateful to those who helped them to attain it for the
Remembering the point about Stephen Hawking, perhaps one day, books that feature equations will have their circulation enhanced by that feature. Perhaps we will know that then, we have an educated citizenry.
The Minister for Lifelong Learning, Further and Higher Education (Alan Johnson): I begin by echoing the comments of my hon. Friend the Member for Hemel Hempstead (Mr. McWalter) on Sir Nicolas Bevan's retirement. I should also like to associate myself with remarks made by Members on both sides of the House throughout the day, and with the sentiments of the well-supported early-day motion. It is not often that a Government representative supports an early-day motion, but I do so on this occasion because it recognises Sir Nicolas's long and distinguished service. I wish him well in his retirement.
I congratulate my hon. Friend the Member for Hemel Hempstead on securing this debate. He said that he was expecting my hon. Friend the Minister for School Standards to reply, and I should point out that there has been a fierce struggle among the seven Ministers in the Department for Education and Skills in that regard. In the end, my hon. Friend was thought to be far too junior. He has a good career in front of him, but he was part of the 2001 intake and is therefore far too young. So I have the honour to reply to today's debate.
I thank my hon. Friend the Member for Hemel Hempstead for defining what quadratic equations actually are. In fact, my Parliamentary Private Secretary provided me with one, and I shall check it with my hon. Friend afterwards to see whether my Parliamentary Private Secretary will continue to hold his post in future. I hope that I can provide my hon. Friend with a repudiation of the comments, made on the radio a couple of weeks ago, of the trade union leader to whom he referred.
Quadratic equations allow us to analyse the relationships between variable quantities, and they are the tool for understanding variable rates of change. It is in variable rates of change that quadratic equations are seen in economics, science and engineering. Examples of the use of quadratic equations include acceleration, ballistics and financial comparisons. Most drivers would feel capable of working out whether they can overtake the car in front, but do they realise that they are solving a quadratic equation in doing so? I dare say that many do not. In fact, it is claimed that the Babylonians, in 400BC, were the first to use the notion of quadratic equations in problem solving, although at the time they had no idea what an equation was.
In preparing for this debate, the DFES conducted a straw poll involving a 16-year-old who had just sat maths GCSE, a head of maths and an experienced chemical engineer. The 16-year-old thought that quadratic equations were logical and fairly straightforward because
The place of quadratic equations in everyday life is pretty clear, but what are pupils taught at school? The national numeracy strategy has had a significant impact on raising the standards of mathematics in primary schools. Last year's key stage 2 results showed that 73 per cent. of pupils achieved the expected level for their age in mathematics, which is a 14 per cent. increase since 1998. We want to build on that impressive record, which is why we have launched "Excellence and EnjoymentA Strategy for Primary Schools". Our vision for primary education is of excellence and enjoyment at the heart of a broad and rich curriculum.
The key stage 3 national strategy for 11 to 14-year-olds provides a comprehensive professional development programme for teachers, new materials and support from expert local consultants. The maths teaching framework emphasises the development of algebraic reasoning. It encourages pupils to develop an understanding of how algebra is a way of generalising from arithmetic, and to represent problems and solutions in a variety of forms.
Simple linear equations are taught from key stage 3. In 2002, key stage 3 results stand at their highest ever, with 67 per cent. of pupils achieving level 5 plus in the key stage 3 tests for both maths and science. Quadratic equations, with their more complex parabolic curves, are taught from late key stage 3 or key stage 4. Factorisation of algebra is a difficult concept to understand and students need plenty of practice. Teaching students to think logically and to analyse different problems is a very important skill, which is not only transferable to other areas of the curriculum but can be used beyond student life. [Interruption.] The hon. Member for Epping Forest (Mrs. Laing) from a sedentary position reminds us of that as I speak.
Pupils taking the intermediate tier GCSE mathematics study algebraic manipulation, including the solving of quadratic equations. They are covered in greater depth by pupils following the higher tier GCSE course and developed further for those going on to study maths on A and AS-level courses. It is at that level that students are taught the concepts that they will need, should they choose to do degrees in maths, sciences, engineering or economics.
There is a shortage of people nationally who can construct these mathematical models and who understand them enough to use them. The fact that an inquiry is taking place into post-14 mathematics is a testament to the importance of the subject. The aims of the post-14 inquiry, announced in July 2002, are to
The use of information and communications technology in schools and in teaching and demonstrating mathematics models is helping the understanding of all learners. With ICT becoming a more integral part of classroom teaching, students can visualise and problem-solve in more creative ways. Those, too, are lifelong skills that can be applied in daily life, not just as a student. ICT gives students confidence in their abilities and increases their eagerness to learn. Using graphical calculators to learn about quadratic functions, for example, helps pupils learn in a more innovative environment.
Several interesting initiatives support teachers in making maths lessons more challenging and exciting. I should like briefly to describe them. Census at school can be used in a number of curriculum subjects, particularly maths. Pupils fill out a questionnaire, see how a census works and are able to compare their school's results with those of other schools in the UK and elsewhere. That is particularly helpful for key stage 3 pupils encountering data and learning how to handle them.
The UK mathematics trust works with secondary school teachers and pupils to promote mathematics. It encourages all secondary schools to take part in competitions and events, including the team maths challenge. The trust also identifies and trains students for the international mathematics olympiad.
The work of the Cambridge university-based millennium maths project allows teachers and students to tap into resources over the internet. Students can ask university undergraduates for help with mathematical problems. The project also offers tailored and continuous professional development for teachers.
The intake to initial teacher training courses in mathematics rose to 1,670 in 200203, an increase of 8 per cent., and an overall increase of 28.5 per cent. since 19992000. The number of graduates applying to train as teachers of mathematics on post-graduate certificates in education courses in 200304 was 35 per cent. higher than for the same period last year. In a recent Ofsted report, it was noted that today's newly qualified teachers are the best trained ever. We need not only to continue to increase the number of teachers, but to support mathematics subject specialism. We want teachers to maintain their enthusiasm for maths and to develop their expertise throughout their careers.
In March, my right hon. Friend the Secretary of State for Education and Skills announced that Adrian Smith would advise on options and costs for a national centre for excellence in mathematics later this year. The new centre should harness all the good work already under way and enable more teachers to tap into the resources and support that they need.
In conclusion, the teaching of quadratic equations, and of the mathematics curriculum overall, is key to a future work force that can develop and use mathematical models in daily life. As research in a book of quotations reveals, Napoleon said: